14th Australasian Fluid Mechanics Conference Adelaide University, Adelaide, Australia 10-14 December 2001

Numerical And Experimental Investigati

Condensing Flow of Steam in L

M.Z. Yusoff1, Z.A. Mamat2, F. Bakhtar3, I. Huss1Department of Mechanical

Universiti Tenaga Nasional, Selang 2Power Plant Technology Unit, T

Kajang, Selangor, 4303School of Manufacturing and Mech

University of Birmingham, Edgbaston, Birm

Abstract The present paper describes a work that has been undertaken to study the effect of wetness in Low Pressure (LP) steam turbines cascade theoretically and experimentally. Theoretical treatments are done by combining the equations describing the behavior of the droplets with the gas dynamic equation. The gas dynamic equation is solved using time marching method applied to cell-vertex type finite volume. In order to reproduce realistic high speed condensation process as in turbine, test are done in a blow down steam tunnel which is capable of producing supercool steam without giving kinetic energy. The predicted results are compared with the experiments. It is shown that the agreement is very good. Introduction In the course of steam expansion in a turbine, the state path crosses the saturation line and the fluid first supercools and then nucleates to become a two-phase mixture. The subsequent two-phase flow of steam through the final stages of turbines poses a number of problems, which are not encountered in other turbomachines. In conventional power plant, the wetness levels in the last few stages of the LP turbines can be as high as 10 - 12 %. It is agreed in the literature that the nucleating and wet stages of steam turbines are less efficient than those running with superheated steam. This reduction in efficiency is attributed collectively to wetness loss, but the mechanisms which give rise to them are insufficiently understood. The present paper describes a work that has been undertaken to study the effect of wetness in Low Pressure (LP) steam turbines both experimentally and theoretically. Firstly, the condensation and wetness problems in LP turbines will be reviewed. Then, the theoretical model adopted is described. This is followed by the descriptions of the experimental setup and measurements. The predicted results will be compared with those obtained from experiments. Condensation and Wetness Problems in Turbines The effects of the presence of liquid phase on the efficiency of steam turbines has been recognised since the early days. As early as 1912, Baumann [1] proposed his famous one percent for one percent rule, in which he suggested that the efficiency of a turbine stage decreases by one percent for each percent of water present. Erosion is a tangible consequence of the presence of liquid in steam and was first observed in 1920’s. Erosion was caused mainly by droplets impacting on the blades. Erosion is only one consequence of the presence of wetness in turbines. The other consequences are those leading to loss of output. These can be categorised into three separate families; mechanical, thermodynamic and aerodynamic.

The mstator nucleacombithrougand arsteam.droplethe nenegativleadingstrongwhere fundamerosionturn dconden The seirreverlatent the drodifferelosses into thsupercproble It has takes pof hetehave bobservhomogwithinhave measucondenregioneffectsHowevcould expansvery liconden Gyarmmain followwouldsuperhfor nu

869

on of High Speed Two-Phase P Turbine Cascade

ein1, M.H. Bosrooh1, Z. Ahmad1 Engineering, or, 43009 MALAYSIA NB Research Sdn. Bhd.

00, MALAYSIA anical Engineering, ingham B15 2TT, ENGLAND

echanical losses consist of the deposition of droplets on the and rotor blades and drag of the droplets. The droplets ted within the steam deposit on the stator blades by the nation of direct inertial impaction and turbulent diffusion h the boundary layer. They then form into films and rivulets e driven to the trailing edges of blades by the drag of the They are then re-entrained into the flow in the form of large ts having a low absolute velocity. These droplets impinge on xt rotor blades with large relative velocities and high e incidence exerting a braking effect and eroding the edges. Water deposited on the rotor blades, is subject to

centrifugal forces and moves towards the tip of the blades, it is flung off in a radial direction. However, the more ental issue is the source of the liquid droplets causing the damage, that is the deposition of finer droplets which in

epends on the size of droplets formed during spontaneous sation.

cond family is thermodynamic losses. These result from sible heat transfer across finite temperature differences. The heat, released during condensation is transferred back from plet surfaces to the parent vapour across a finite temperature nce and causes a rise in entropy. The third aspect of the is the aerodynamic repercussions of the release of latent heat e flow. The effect of the pressure rise due to condensation, ritical instability and choking on the flow are among the ms.

been generally assumed that condensation within turbines lace through spontaneous condensation and the possibility rogeneous condensation has been excluded. However, there een reports in the literature of cases where wetness was ed well in advance of Wilson line. This suggests that, eneous nucleation is not the sole mean of droplet formation a real turbine. Some other mechanisms of condensation been suggested to explain the phenomena. On site rements by Steltz et al. [2] have indicated the presence of sate containing high concentrations of impurities in the

s of the saturation lines, suggesting that heteromolecular may play some role in the appearance of the liquid phase. er, it is improbable that the large droplet sizes observed provide enough inter-phase surface area to allow further ion to proceed close to thermodynamic equilibrium. It is kely that, the bulk of the flow will experience homogeneous sation when the Wilson line is reached.

athy [3], considered possible temperature fluctuations in the stream and suggested that some packets of stream would more efficient paths through the turbines than others and consequently cool more rapidly. His theory only refers to eated flows. Bakthar and Heaton [4] investigated this effect cleating flows in steam turbines. They suggested that some

of the packets may supercool sufficiently to nucleate when the average flow has still not attained this condition. However, later, Moore et al. [5], conducted nozzle experiments using a grid in the inlet plane to generate turbulence, and found a practically identical pressure distribution and droplet sizes with and without the grid. They therefore concluded that, flow fluctuations were unlikely to be responsible for early nucleation. Moore later, argued that, early nucleation in turbines occurs on the curved surface of blade due to over-expansion and the nuclei formed can spread out to other regions to seed the flow, thus providing centres for condensation. In the case of turbines, it has also been suggested that, unsteady flow due to super-critical heat addition may be responsible for increased loss due to boundary layer separation and may even be responsible for blade failures. However, no evidence is available, and it is not known whether the phenomenon occurs in two and three-dimensional flows. Considering all the above, it can be concluded that the most significant condensation process will be the spontaneous or homogeneous condensation. Thus the model developed in the present work assumed that condensation occurs solely via this mechanism. Numerical Treatment of Two-Phase Condensing Flow In order to predict the behaviour of nucleating and wet steam flows the equations describing the droplet behaviour have to be combined with the standard gas dynamic equations and treated as a set. The governing gas dynamics equation is the Euler equation written in strong intergral conservation form as shown below :

( )∫ −−=∂∂Ω

SCC dxGdyF

tw

where Ω, is a fixed area of the finite volume with boundary S. w represents the conserved variables,

CF and CG are the fluxes in

x- and y-directions. These may be expressed as : -

ρρρρ

=

0

y

x

eVV

w

,

ρ

ρ+ρ

ρ

=

0x

yx

2x

x

C

hVVV

PV

V

F

,

ρ+ρ

ρρ

=

0y

2y

xy

y

C

hV

PV

VV

V

G

,

eo and ho are the specific total internal energy and specific total enthalpy of the fluid respectively. In the usual notations : -

2Vee

2

0 += and 2

Vh2

0 +=h

where . The above set of equations are solved using

time-marching method. The right hand side of the equation is applied directly to each cell vertex type finite control volume. The spatial discretizations are performed using second order central differencing. This is followed by marching in time until the solution converges.

2y

2x

2 VVV + =

The Euler equations are applicable to two-phase flows without alteration providing the fluid properties ρ, h and e refer to the overall mixture and the pressure, P, is that of the vapour phase. Two-phase effects are introduced into the governing equations by the introduction of the wetness fraction, w , defined as : - ( )

( ) ( )liquidofmassvapourofmassliquidofmass

+=w .

The enthalpy and specific volume of the mixture may be written as

LG whh)w1(h +−=

Subscrand sy The wfrom tof the

The raand thend ofexistinformedincrem The nufrom tflow to

The nu

sJ

The siKelvinoefc fic (1)

The rconsidvapourtime in

where step thtaking

(2)

In ordequatiocoefficcoeffic

where,consta ExperAt lownucleahas preconditconvenof nucin coninitiallbladinsubsonbe repr

(3)

(4)

870

LG

1w1)w1(1ρ

+ρ

−=ρ

(5)

ipts G and L refer to vapour and liquid phases respectively mbols without subscript refer to the whole mixture.

etness fraction at any point in the flow field is calculated he averaged radius, r , and number of droplets per unit mass mixture, N : -

L

3Nr

34 ρπ=

w . (6)

dius is obtained from nucleation and droplet growth laws e total number of droplets per unit mass of the mixture at the a calculation step is the sum of the number of droplets g within the flow initially, 1 , and the number of new nuclei due to spontaneous nucleation,

N

nucN , over the time ent, δt. Thus : -

nuc1 NN +=N (7)

mber of newly nucleated droplets, nucN can be determined he nucleation current, J and the time increment, δt, for the transverse the step , i.e. :

st

t JN stnuc δ= . (8) cleation current, is given by : stJ

( )

∆−ρ

ρρπ

σ+

=G

*

L

GGS3

rt kT

G exp Tm

2qv1

1

volume.secnuclei (9)

ze of new droplets is related to the vapour conditions by -Helmholtz relation modified to include the second virial

: - ient

( ) ( )( )

ρ−ρ+

ρ

ρρ

σ=

GSGS

GL

r*

TB2T

lnRT

2r

(10)

ate of growth of the droplets can be calculated by eration of heat transfer between the droplet and its parent . The radius, r , of a droplet with an initial radius of r1 after a terval, δt, is obtained from the equation : -

( ) ( ) t drrrrlncrrbrr

2 *1

*

12

12 δ=

a

−−+−+−

a, b, c and d are constant coefficients. At the end of each e old and new droplets are combined into one population by the root mean square.

(11)

er to take into account of real fluid effect, appropriate n of state for steam is used. The equation used is the virial ient equation of state truncated after the first virial ient. i.e. :

G

GG

B1RTP ρ+=

ρ (12)

ρG, TG and R are the vapour density, temperature and gas nt respectively and B is the second virial coefficient.

imental Setup And Measurements and moderate pressures, initially saturated steam will not

te substantially when expanded to sonic condition. This fact cluded the experimental reproduction of nucleating and wet

ions found in steam turbines. Studies of nucleation have tionally been carried out in steady state tunnels with zones

leation arranged to occur in areas of supersonic flow. This is trast to the flow in steam turbines where much of the energy y possessed by the steam is extracted as work by the turbine g and therefore the fluid can nucleate when the flow is ic. Thus nucleating conditions occurring in turbines cannot oduced satisfactorily in steady state tunnels

In order to achieve satisfactory nucleation in a subsonic flow, it is necessary to procure a supply of supercooled steam. Supercooled steam will nucleate after experiencing a slight expansion and thus does not need to be accelerated to sonic condition. The general features of the blow down facility are shown diagramatically in figure (1). The receiver is a pressure vessel which holds the supply of supercooled steam for blow down. The external walls of the receiver are lagged to prevent heat loss, and inside an aluminium inner shield protects the steam from the higher wall temperatures. Water sprayers positioned between the shield and outer walls can be used to control the wall temperature.

Valve (QAV) is a quick acting valve driven by a pneumatic impact cylinder. When open, the valve allows steam to flow from the receiver to the test section. Valve (BV) is a butterfly valve used for setting the test section back pressure in subsonic tests. The spent steam is discharged to the condenser.

Despite the presence of the aluminium inner shield the heat transfer between the receiver walls and the steam imposes a limit on the maximum supercooling attainable. This problem is overcome by using bypass (A, B and C) between the receiver and condenser. These allow a higher discharge rate and therefore less time for heat transfer to take place as the expansion of the steam in the tank is much more rapid. The principle of operation of the equipment can be illustrated using the enthalpy-entropy diagram shown in figure (2). If the receiver is initially charged, and then vented to the condenser, the steam remaining in the tank has to expand. Considering the expansion between P1 and P2 in the superheated region as shown by AB, the fluid will be less superheated at B than at A. If the steam is free from foreign particles then expansion from an initially saturated state along EF will cause the steam to supercool without accelerating the flow during the expansion. By selecting appropriate expansion ratio (P1/P2) various levels of supercooling may be selected. The blades making up the cascade are mounted on supporting plates forming an assembly which is then fitted into the test section. The flow passage through a rotor blade cascade assembly is shown in figure (3). The central two blades in the cascade are mounted as a separate interchangeable unit. Different units exist

for proutlet boardsblade p

ResulExperiinlet to1.49. Mpressucorrespin addipaper, and cofeatureprogra

Fig. (1) : General Features of the Blow Down Facility

Fi Fig. (2) : Expansion Path of Steam

A comand mflow ashowsphotogcompawith thMach-numbeseen tpressusurfacepressuaccura The cothe nuconstasurfacesuperhmid-papressuwith thsuddenthroug

871

essure and optical measurements. In supersonic tests the pressure of the cascade is set using two adjustable solid tail pivoting from the trailing edges of the upper and lower rofiles.

Fig. (3) : Linear Cascade Test Section

ts mental measurements have been carried out for the overall tal to outlet static pressure ratios of 3.05, 2.32, 1.83 and easurements were recorded at a constant inlet stagnation

re of 1.3 bar and a number of different inlet temperatures onding with 0, 7, 15 and 21 K nominal inlet supercoolings tion to one giving completely superheated flow. In this only the results at pressure ratio of 2.32 will be discussed mpared with numerical calculation to illustrate the important s of nucleating flow of steam and ability of the prediction m.

Suction Surface Pressure Surface Mid Passage

g. (4) : Comparisons of Measured and Calculated Static Pressure Distribution – Superheated Flow

parison between the theoretical and experimental surfaces id-passage line static pressure distributions for superheated t pressure ratio of 2.32 is shown in figure (4). Figure (5a) the contours of constant Mach number. A Mach-Zhender raph obtained from experiment is included for direct rison. The theoretical static pressure distributions agree well e measurements. The overall flow features as shown by the

Zhender photograph agree well with the calculated Mach r variations within the passage. Two shockwaves can be o originate from the trailing edge. The shockwave on the re side crosses the passage and impinges on the suction at about 80 % axial chord and causes a rise in static

re. The magnitude of the rise in pressure has been predicted tely.

rresponding comparison of static pressure distributions for cleating solution are shown in figure (6) and the contours of nt Mach number are given in figure (5b). On the pressure , the distributions are very similar to those of the eated test. But a substantial difference can be observed at the ssage line and on the suction surface. There is a steep

re rise at about 77 % axial chord which corresponds well e experimental data. This rise in pressure is caused by the release of latent heat as the flow reverts to equilibrium h rapid condensation. The magnitude of the pressure rise has

been slightly under-predicted. Downstream of the rapid condensation zone, experimental data show another pressure rise at about 0.85 axial chord caused by the pressure side trailing edge shockwave impinging on the suction surface. This has not been predicted by the calculation perhaps due to shock smearing where the mesh is highly non-orthogonal. The overall flow features agree well with the experimental observation. The shock structure near the pressure side of the trailing edge is difficult to interpret because it coincides with the onset of rapid condensation.

The distributions of nucleation rate and droplet radius on the pressure, suction surfaces and mid-passage line are shown in figures (7) and (8) respectively. Contours of constant supercooling and wetness fraction are shown in figures (9a) and (9b) respectively. On the suction surface, the supercooling increases rapidly as the flow accelerates in the blade passage. At about 55 % axial chord, supercooling reaches 25 K, nucleation becomes significant and droplets start to form. Further downstream, nucleation rate increases rapidly and more droplets are formed. But the radius remains small and the flow continues to supercool. At about 80 % axial chord, supercooling reaches 40 K, the Mach number is 1.076 and the flow cannot sustain any more supercooling and breakdown of supersaturation occurs with rapid condensation. No more droplets are formed and the number of droplet remains constant. Droplet radius and wetness fraction rapidly increase. The nucleation rate drops sharply as the flow reverts to equilibrium. At the trailing edge, when the flow crosses a shockwave, it becomes superheated to nearly 20 K. This causes the droplets to evaporate and decrease in size and the wetness fraction to decrease.

On the pressure surface, the supercooling remains low until very close to the trailing edge. The supercooling, nucleation rate and number of droplets rise sharply until rapid condensation occurs at about 50 K supercooling at a Mach number of 1.253. This sharp expansion rate leaves little time for the droplets to grow and a very large number of fine droplets are formed. It can also be seen that the locus of maximum supercooling coincides well with the

observzone ivariatipitch dDownsHowev

a. Dry b. Nucleating

Fig. (5) : Predicted Mach Number Contours For Dry and Nucleating Flow Together with Mach Zhender Photographs Conc

From develonucleareleasethe ext

a. Su

Fig. ( Refer [1] B Pr[2] St CoSuction Surface

Pressure Surface ThMid Passage [3] Gy

Me Tu[4] BaFig. (6) : Comparisons of Measured and Calculated Static Pressure

Distribution – Nucleating Flow We dyn[5] Mo the and

872

ed rise in pressure associated with the rapid condensation n the contours of constant Mach number. Also, considerable ons exist in wetness fraction and droplet radius across the ue to different thermodynamic paths followed by the fluid. tream of the blade, the droplet radius varies significantly. er the wetness fraction remains approximately uniform.

Fig. (7) : Nucleation Rate

Suction Surface Pressure Surface Mid Passage

Fig. (8) : Droplet Radius

Suction Surface Pressure Surface Mid Passage

lusions the results it can be concluded that the theoretical treatment ped is capable of predicting the location of the onset of tion as well as the magnitude of the pressure rise due to the of latent heat to the parent vapour. Futher work would be ension to three dimensional flow.

b. Wetness Fractionpercooling

9) : Contours of Constant Supercooling and Wetness Fractions

ences aumann, K., Some Recent Developments in Large Steam Turbine actice, J. Inst. Elec. Engrs., 48: 768-877, 1912 eltz, W.G., Lee, P.K. and Linsay, W.T., The Verification of ncentrated Impuritites in Low Pressure Steam Turbines, e Winter Annual Meeting, ASME, 1981 armathy, G.,Discussion on 'Flow Unsteadiness and Turbulence asurements in the Low Pressure Cylinder of a 500 MW Steam rbine’ by Wood, N.B. . Inst. Mech. Engrs., C54/73, 1973 khtar, F. and Heaton, A.V., 'A Theoretical Comparative Study of tness Problems in a Model and Full-Scale Turbine, Aerothermo- amics of Steam Turbines, ASME Winter Annual Meeting, 1981 ore, M.J., Walters, P.T., Crane, R.I. and Davidson, B.J.'Predicting Fog-Drop Size in Wet Steam Turbines', Inst. Mech. Engrs., Heat Fluid Flow in Steam and Gas Turbine Plant, 1973.